Theorems · Theorem · measure theory
Metric.measure_closedBall_pos
∀ {X : Type u_1} [inst : PseudoMetricSpace X] {m : MeasurableSpace X} (μ : MeasureTheory.Measure X) [μ.IsOpenPosMeasure]
(x : X) {r : ℝ}, 0 < r → 0 < μ (Metric.closedBall x r)See also Metric.measure_closedBall_pos_iff.
- Defined in
- Mathlib.MeasureTheory.Measure.OpenPos
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Realstatement and proof · cited by 25,697
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- PseudoMetricSpacestatement and proof · cited by 1,550
- Metric.closedBallstatement · cited by 704
- LT.lt.trans_leproof · cited by 678
- MeasureTheory.measure_monoproof · cited by 338
- MeasureTheory.Measure.IsOpenPosMeasurestatement and proof · cited by 80
- Metric.ball_subset_closedBallproof · cited by 46
Cited by8
Results whose statement or proof uses this declaration.
- MeasureTheory.addHaar_image_le_mul_of_det_ltproof · cited by 4
- ApproximatesLinearOn.norm_fderiv_sub_leproof · cited by 3
- AddCircle.ae_empty_or_univ_of_forall_vadd_ae_eq_selfproof · cited by 2
- MeasureTheory.Measure.tendsto_addHaar_inter_smul_one_of_density_one_auxproof · cited by 1
- ContDiffBump.normed_le_div_measure_closedBall_rOutproof · cited by 1
- Metric.measure_closedBall_pos_iffproof · cited by 0
- ContDiffBump.normed_le_div_measure_closedBall_rInproof · cited by 0